7 papers
On the distribution of the total number of generators of -free and -full elements in an abelian monoid
Sourabhashis Das, Wentang Kuo, Yu-Ru Liu
Let be an element of an abelian monoid, with denoting the total number of prime elements generating . We study the moments of $Ω(\m…
An effective version of Chebotarev's density theorem
Sourabhashis Das, Habiba Kadiri, Nathan Ng
Chebotarev's density theorem asserts that the prime ideals are equidistributed among the conjugacy classes of the Galois group of any normal extension of number fields. An effectiv…
New zero-free regions for Dedekind zeta-functions at small and large ordinates
Sourabhashis Das, Swati Gaba, Ethan Simpson Lee +2
Given a number field , we obtain new and explicit zero-free regions for Dedekind zeta-functions of , which refine the previous works of Ahn--Kwon, Kadiri, and…
A subset generalization of the ErdÅs-Kac theorem over number fields with applications
Sourabhashis Das, Wentang Kuo, Yu-Ru Liu
Let denote the number of distinct prime factors of a natural number . In 1940, ErdÅs and Kac established that obeys the Gaussian distribution over natural numbe…
Generalizations of ErdÅs-Kac theorem with applications
Sourabhashis Das, Wentang Kuo, Yu-Ru Liu
Let denote the number of distinct prime factors of a natural number . In 1940, ErdÅs and Kac established that obeys the Gaussian distribution over natural numbe…
On the distribution of the number of distinct generators of h-free and h-full elements in an abelian monoid
Sourabhashis Das, Wentang Kuo, Yu-Ru Liu
This work introduces the first in-depth study of h-free and h-full elements in abelian monoids, providing a unified approach for understanding their role in various mathematical st…